© A.W.Marczewski 2002

A Practical Guide to Isotherms of ADSORPTION on Heterogeneous Surfaces

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## How to calculate surface charge from titration data

### Figures: titration curves | acid/base balance

See also experimental example of soil titration and data analysis Titration curves - acid/base balance
Calculation of base/acid balance from the titration data of soil (sample mass: 0.5 and 1.0g) - the balance of base/acid for soil sample is compared to the balance of base/acid for blank sample (same as for suspension, but without solid) for a given pH.
The Δnsol,H+ , required in order to calculate surface charge, may be calculated by comparing the balance of protons and hydroxyl ions in titration of solid with electrolyte titration: where solution acid/base balance (Vtotal is usually slightly different for electrolyte and solid titrations because various amounts of acid and base must be added in order to reach the same pH value):  Acid/base consumption vs. sample mass (fixed pH = 4)
The differences in acid/base consumption balance are used to calculate surface charge (from the slope) and acid/base consumption for sample dissolution (assumption - the solution is saturated with dissolved sample matter (e.g. sample impurities or sample matter itself) for the smallest sample mass used in this plot. If only 1 sample mass is used, there is no way to evaluate what part of acid/base consumption is spent on charging the sample surface and how much is spent on other chemical reactions ("sample dissolution" part) (see more on possible causes).

If the balance is proportional to the sample mass, i.e. no dissolution (or any other non-charging chemical reaction) occurs, i.e. the entire difference in acid/base consumption is spent on the surface charge: (This is also true, if some component of the sample reacts with acid/base and no saturation is observed for the sample amounts used!)
From the last equation we have surface charge: where: n - acid/base balance per sample ([mol] or [mmol]), F is Faraday constant (F=96500 C/mol), m - sample mass [g], SBET - surface area [m2/g]; qs is usually expressed as [C/m2] or µC/cm2.

If the balance is NOT proportional to the sample mass in the result of sample reaction, dissolution of impurities etc., then: where Δno,k is the pH-dependent amount of acid/base spent on very small sample (extrapolated to the zero mass, assuming the same course of the plot

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